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from IPython.core.display import display, HTML
display(HTML("<style>.container { width:95% !important; }</style>"))
import numpy as np
import pandas as pd
import sklearn
import matplotlib.pyplot as plt
import plotly.express as px
Task 1¶
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Musk = pd.read_csv("Musk1.csv", header = None)
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Musk.head()
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Musk_Feat = Musk.iloc[:,2:Musk.shape[1]]
a.¶
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from sklearn.decomposition import PCA
from sklearn.manifold import MDS
from sklearn.preprocessing import scale
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
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Musk_Feat = Musk.iloc[:,2:Musk.shape[1]]
Musk_Feat = pd.DataFrame(scale(Musk_Feat),columns=Musk_Feat.columns)
# mds
mds = MDS(n_components=3)
musk_mds = pd.DataFrame(mds.fit_transform(Musk_Feat))
# pca
pca = PCA(n_components=3)
musk_pca = pd.DataFrame(pca.fit_transform(Musk_Feat))
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# join labels
musk_mds = musk_mds.join(Musk.iloc[:,0],rsuffix = "_label")
musk_pca = musk_pca.join(Musk.iloc[:,0],rsuffix = "_label")
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musk_pca = musk_pca.rename(columns = {'0': "pc_1", 1: 'pc_2', 2: 'pc_3',"0_label" : "label"})
musk_mds = musk_mds.rename(columns = {'0': "latent_1", 1: 'latent_2', 2: 'latent_3',"0_label" : "label"})
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musk_pca["label"] = musk_pca["label"].astype(str)
musk_mds["label"] = musk_mds["label"].astype(str)
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musk_pca.head()
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musk_mds.head()
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fig = px.scatter_3d(musk_pca, x="pc_1", y="pc_2", z="pc_3",
color='label', width = 800, height = 800 ,title = "PCA with 3 Components")
fig.show()
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fig = px.scatter_3d(musk_mds, x="latent_1", y="latent_2", z="latent_3",
color='label', width = 800, height = 800 ,title = "MDS with 3 Latent Variables")
fig.show()
- Looking at the graphs, I can't say our assumption is good enough. Because both PCA and MDS is not able to explain the labels with 3 latent variables, since they seem pretty mixed.
b.¶
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Musk = Musk.rename(columns={0: "BAGLABEL", 1: "BAGID"})
Musk = Musk.groupby('BAGID').mean().reset_index(drop=True)
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Musk.head()
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Musk_Feat = Musk.iloc[:,2:Musk.shape[1]]
Musk_Feat = pd.DataFrame(scale(Musk_Feat),columns=Musk_Feat.columns)
# mds
mds = MDS(n_components=3)
musk_mds = pd.DataFrame(mds.fit_transform(Musk_Feat))
# pca
pca = PCA(n_components=3)
musk_pca = pd.DataFrame(pca.fit_transform(Musk_Feat))
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# join labels
musk_mds = musk_mds.join(Musk.iloc[:,0],rsuffix = "_label")
musk_pca = musk_pca.join(Musk.iloc[:,0],rsuffix = "_label")
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musk_pca = musk_pca.rename(columns = {0: "pc_1", 1: 'pc_2', 2: 'pc_3',"BAGLABEL" : "label"})
musk_mds = musk_mds.rename(columns = {0: "latent_1", 1: 'latent_2', 2: 'latent_3',"BAGLABEL" : "label"})
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musk_pca["label"] = musk_pca["label"].astype(str)
musk_mds["label"] = musk_mds["label"].astype(str)
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musk_pca
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fig = px.scatter_3d(musk_pca, x="pc_1", y="pc_2", z="pc_3",
color='label', width = 800, height = 800 ,title = "PCA with 3 Components")
fig.show()
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fig = px.scatter_3d(musk_mds, x="latent_1", y="latent_2", z="latent_3",
color='label', width = 800, height = 800 ,title = "MDS with 3 Latent Variables")
fig.show()
- When we take the average our dimensionality reduction methods seem to give better results. They are not seperated randomly as it was before. This supports my claim that our assumption was not good enough.
c.¶
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from statistics import mode
- Another approach might be taking the most common one (mode). The custom function below finds the most common element in the array. If there is more then one, then it returns the average of them.
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def most_common(x):
try:
return(mode(list(a)))
except:
temp = pd.DataFrame(data = {'level': x, 'countno' : np.repeat(1, len(x))})
temp = temp.groupby("level").count().reset_index()
temp["maxvalue"] = temp.countno.max()
return(temp.loc[temp.countno == temp.maxvalue].level.mean())
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Musk = pd.read_csv("Musk1.csv", header = None)
Musk = Musk.rename(columns={0: "BAGLABEL", 1: "BAGID"})
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Musk = Musk.groupby('BAGID').agg(lambda x: most_common(x))
- Musk data below is in format of figure 1.
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Musk.head()
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Task 2¶
1.¶
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import matplotlib.image as mpimg
import matplotlib.pyplot as plt
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img = mpimg.imread('Foto_256_256.jpg')
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plt.imshow(img)
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2.¶
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from copy import deepcopy
img_noise = deepcopy(img)
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MinPixel = img_noise.min()
MaxPixel = img_noise.max()
img_noise = img_noise + np.random.randint(MinPixel,(MaxPixel * 0.1),size = img_noise.shape)
# max value cannot exceed 255
img_noise[img_noise >= 255] = 255
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plt.imshow(img_noise)
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img_noise_red = deepcopy(img_noise)
img_noise_green = deepcopy(img_noise)
img_noise_blue = deepcopy(img_noise)
img_noise_red[:,:,1] = 0
img_noise_red[:,:,2] = 0
img_noise_green[:,:,0] = 0
img_noise_green[:,:,2] = 0
img_noise_blue[:,:,0] = 0
img_noise_blue[:,:,1] = 0
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fig, ax = plt.subplots(ncols = 2, nrows = 2, figsize = (15,15))
ax[0,0].imshow(img_noise)
ax[0,0].set_title("Original")
ax[0,1].imshow(img_noise_red)
ax[0,1].set_title("Red Channel")
ax[1,0].imshow(img_noise_green)
ax[1,0].set_title("Green Channel")
ax[1,1].imshow(img_noise_blue)
ax[1,1].set_title("Blue Channel")
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3.¶
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# https://stackoverflow.com/questions/12201577/how-can-i-convert-an-rgb-image-into-grayscale-in-python
img_grayscale = np.dot(img_noise[...,:3], [0.2989, 0.5870, 0.1140])
plt.imshow(img_grayscale)
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from sklearn.feature_extraction import image
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patches = image.extract_patches_2d(img_grayscale, (25, 25))
patches = patches.reshape((53824,625))
a.¶
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pca = PCA(n_components = 100)
pca.fit(patches)
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from plotnine import *
pca_cumvar = pd.DataFrame(data = {'PC' : np.arange(1,len(pca.explained_variance_ratio_) + 1), 'CUMVAR' : pca.explained_variance_ratio_.cumsum()})
ggplot(pca_cumvar) + geom_line(aes(x = "PC", y = "CUMVAR" ), colour = "r")
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pca_cumvar.head()
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- Looking at the graph we can say that after 25th marginal utility (proportion of ratio that covers) of principal components is decreased significantly. Another impportant inference is that first principal component explains 0.62 of the total variance.
b.¶
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pca_im = PCA(n_components = 3)
principals = pca_im.fit_transform(patches)
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fig, ax = plt.subplots(1,3,figsize = (25,25))
for i in range(3):
im_comp = principals[:,i].reshape(232,232)
ax[i].imshow(im_comp)
ax[i].set_title("Component {}".format(i+1))
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pca_im.explained_variance_ratio_
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- Considering the difference between 3 components in terms of their variance explaination, I would expect 1st image to be more apperant compared to others. But still main frame of the image is clearer then the others.
c.¶
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fig, ax = plt.subplots(1,3,figsize = (25,25))
for i in range(3):
eigen = pca_im.components_[i].reshape(25, 25)
ax[i].imshow(eigen)
ax[i].set_title("Eigenvector {}".format(i+1))
- These reshaped version of eigenvectors actually represent typical patches. Different combination of them may help us reconstruct an image which close to the original one.